Adams, Peter and Eggleton, Roger and MacDougall, James A. (2009) *Graphs which are linked cycles.* Congressus Numerantium, 195 .

## Abstract

A graph H of order h is an n-linked cycle if it has an induced subgraph G of order g < h and an automorphism Î±: H â�� H of order n â�¥ 2 such that H = â��{Î±r(G) : 0 â�¤ r < n} and G has an induced subgraph K of order k < g such that Î±r(G) â�� Î±râ�ºÂ¹(G) â�� K for 0 â�¤ r < n. Then G is the initial link of this linked cycle, K is its kernel, Î±|G is the link isomorphism, and any pair (G, Î±) allowing H to be expressed as a linked cycle yields a generalized factorization of H. For a given standard ordering of all finite graphs, the "earliest" pair (G, Î±) is a fundamental representation of H. There are 2 593 574 linked cycles among all graphs of order h â�¤ 10. The paper gives an overview, and a fundamental representation of each of them is provided on a supporting website.

Item Type: | Article |
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Uncontrolled Keywords: | graph automorphism, factorization, linked cycle |

Subjects: | UNSPECIFIED |

Faculty: | UNSPECIFIED |

Depositing User: | Dr David Allingham |

Date Deposited: | 28 Sep 2012 12:05 |

Last Modified: | 28 Sep 2012 12:05 |

URI: | http://docserver.carma.newcastle.edu.au/id/eprint/1154 |

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